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MathsAges 13-15

Linear equations

Solve a linear equation by reversing addition and multiplication, then substitute your answer to check it. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 3x + 4 = 19.

    LHS=RHS
    3 · 4 · 19 · Linear equations

  2. 2. Solve 5x + 1 = 101.

    LHS=RHS
    5 · 1 · 101 · Linear equations

  3. 3. Solve 7x + 25 = 109.

    LHS=RHS
    7 · 25 · 109 · Linear equations

  4. 4. Solve 3x + 11 = 47.

    LHS=RHS
    3 · 11 · 47 · Linear equations

  5. 5. Solve 10x + 1 = 41.

    LHS=RHS
    10 · 1 · 41 · Linear equations

  6. 6. Solve 11x + 27 = 38.

    LHS=RHS
    11 · 27 · 38 · Linear equations

  7. 7. Solve 2x + 11 = 51.

    LHS=RHS
    2 · 11 · 51 · Linear equations

  8. 8. Solve 7x + 15 = 148.

    LHS=RHS
    7 · 15 · 148 · Linear equations

  9. 9. Solve 12x + 9 = 165.

    LHS=RHS
    12 · 9 · 165 · Linear equations

  10. 10. Solve 3x + 16 = 31.

    LHS=RHS
    3 · 16 · 31 · Linear equations

  11. 11. Solve 7x + 1 = 8.

    LHS=RHS
    7 · 1 · 8 · Linear equations

  12. 12. Solve 3x + 16 = 67.

    LHS=RHS
    3 · 16 · 67 · Linear equations
12 questions · Seed 104729 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 3x + 4 = 19.

    5

    Subtract 4, then divide by 3. x = 5. Check: 3 × 5 + 4 = 19.

  2. 2. Solve 5x + 1 = 101.

    20

    Subtract 1, then divide by 5. x = 20. Check: 5 × 20 + 1 = 101.

  3. 3. Solve 7x + 25 = 109.

    12

    Subtract 25, then divide by 7. x = 12. Check: 7 × 12 + 25 = 109.

  4. 4. Solve 3x + 11 = 47.

    12

    Subtract 11, then divide by 3. x = 12. Check: 3 × 12 + 11 = 47.

  5. 5. Solve 10x + 1 = 41.

    4

    Subtract 1, then divide by 10. x = 4. Check: 10 × 4 + 1 = 41.

  6. 6. Solve 11x + 27 = 38.

    1

    Subtract 27, then divide by 11. x = 1. Check: 11 × 1 + 27 = 38.

  7. 7. Solve 2x + 11 = 51.

    20

    Subtract 11, then divide by 2. x = 20. Check: 2 × 20 + 11 = 51.

  8. 8. Solve 7x + 15 = 148.

    19

    Subtract 15, then divide by 7. x = 19. Check: 7 × 19 + 15 = 148.

  9. 9. Solve 12x + 9 = 165.

    13

    Subtract 9, then divide by 12. x = 13. Check: 12 × 13 + 9 = 165.

  10. 10. Solve 3x + 16 = 31.

    5

    Subtract 16, then divide by 3. x = 5. Check: 3 × 5 + 16 = 31.

  11. 11. Solve 7x + 1 = 8.

    1

    Subtract 1, then divide by 7. x = 1. Check: 7 × 1 + 1 = 8.

  12. 12. Solve 3x + 16 = 67.

    17

    Subtract 16, then divide by 3. x = 17. Check: 3 × 17 + 16 = 67.

12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 3x + 4 = 19.

    LHS=RHS
    3 · 4 · 19 · Linear equations

  2. 2. Solve 5x + 1 = 101.

    LHS=RHS
    5 · 1 · 101 · Linear equations

  3. 3. Solve 7x + 25 = 109.

    LHS=RHS
    7 · 25 · 109 · Linear equations

  4. 4. Solve 3x + 11 = 47.

    LHS=RHS
    3 · 11 · 47 · Linear equations

  5. 5. Solve 10x + 1 = 41.

    LHS=RHS
    10 · 1 · 41 · Linear equations

  6. 6. Solve 11x + 27 = 38.

    LHS=RHS
    11 · 27 · 38 · Linear equations

  7. 7. Solve 2x + 11 = 51.

    LHS=RHS
    2 · 11 · 51 · Linear equations

  8. 8. Solve 7x + 15 = 148.

    LHS=RHS
    7 · 15 · 148 · Linear equations

  9. 9. Solve 12x + 9 = 165.

    LHS=RHS
    12 · 9 · 165 · Linear equations

  10. 10. Solve 3x + 16 = 31.

    LHS=RHS
    3 · 16 · 31 · Linear equations

  11. 11. Solve 7x + 1 = 8.

    LHS=RHS
    7 · 1 · 8 · Linear equations

  12. 12. Solve 3x + 16 = 67.

    LHS=RHS
    3 · 16 · 67 · Linear equations
12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 3x + 4 = 19.

    5

    Subtract 4, then divide by 3. x = 5. Check: 3 × 5 + 4 = 19.

  2. 2. Solve 5x + 1 = 101.

    20

    Subtract 1, then divide by 5. x = 20. Check: 5 × 20 + 1 = 101.

  3. 3. Solve 7x + 25 = 109.

    12

    Subtract 25, then divide by 7. x = 12. Check: 7 × 12 + 25 = 109.

  4. 4. Solve 3x + 11 = 47.

    12

    Subtract 11, then divide by 3. x = 12. Check: 3 × 12 + 11 = 47.

  5. 5. Solve 10x + 1 = 41.

    4

    Subtract 1, then divide by 10. x = 4. Check: 10 × 4 + 1 = 41.

  6. 6. Solve 11x + 27 = 38.

    1

    Subtract 27, then divide by 11. x = 1. Check: 11 × 1 + 27 = 38.

  7. 7. Solve 2x + 11 = 51.

    20

    Subtract 11, then divide by 2. x = 20. Check: 2 × 20 + 11 = 51.

  8. 8. Solve 7x + 15 = 148.

    19

    Subtract 15, then divide by 7. x = 19. Check: 7 × 19 + 15 = 148.

  9. 9. Solve 12x + 9 = 165.

    13

    Subtract 9, then divide by 12. x = 13. Check: 12 × 13 + 9 = 165.

  10. 10. Solve 3x + 16 = 31.

    5

    Subtract 16, then divide by 3. x = 5. Check: 3 × 5 + 16 = 31.

  11. 11. Solve 7x + 1 = 8.

    1

    Subtract 1, then divide by 7. x = 1. Check: 7 × 1 + 1 = 8.

  12. 12. Solve 3x + 16 = 67.

    17

    Subtract 16, then divide by 3. x = 17. Check: 3 × 17 + 16 = 67.

12 questions · Seed 104729 · Age guidance, not curriculum certification